Sam the 7mm Remington magnum is a SHORT magnum. I don't know if its action would accomodate a .375 H&H magnum.
It would, however, do fine with .300 Win Mag and .338 Win Mag. The .338 is a great round if getting kicked really hard makes you feel manly.
If you are a handloader or wildcatter, the .358 Norma and .416 Taylor will fit.